 Mathematics
25 October, 02:09

# In parallelogram mnpq, side mn is seven inches longer than twice the length of side np if the perimeter of mnpq is 68 inches then determine the length of np

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1. 25 October, 02:55
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Opposite sides of a parallelogram are the same length. Let the length of side np = x inches. Side qm is then also x inches. The problem gives the length of side mn in terms of side np as (2*x) + 7 inches. Side pq is then also (2*x) + 7 inches. The perimeter is the sum of all four sides. x + x + [ (2*x) + 7] + [ (2*x) + 7], or 6x + 14 inches. We are given the perimeter measure, so 6x + 14 = 68. Subtract 14 from both sides: 6x = 54. Divide both sides by 6: x = 9 inches. Thus the length of side np is 9 inches.
2. 25 October, 03:04
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Perimeter of a parallelogram = 2 (a+b)

Perimeter of parallelogram mnpq = 68 inches

mn is seven inches longer than twice the length of side np

let the length of np = x

length of mn = 2x + 7

Now,

p = 2 (2x+7+x)

68 = 4x + 14 + 2x

68 = 6x + 14

6x = 68 - 14

6x = 54

x = 9

Thus, the length of np is 9 inches.